Fill in the blanks to follow the steps in solving the equation: 5x−12−6x=−10x+7−1
(4 points)
5x−12−6x=−10x+7−1
Step 1: Combine like terms
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Step 2: Get x-terms on same side of equation
Step 3: Get constants on same side of equation
Step 4: Get the x by itself by using the inverse operation
Step 1: Combine like terms
- x - 5 = - 3x + 6
Step 2: Get x-terms on same side of equation
- x + 3x = 6 + 5
Step 3: Get constants on same side of equation
2x = 11
Step 4: Get the x by itself by using the inverse operation
x = 11/2 or x = 5.5
are you sure?
Apologies for the incorrect response earlier. Let's go through the steps again:
Step 1: Combine like terms
5x - 12 - 6x = -10x + 7 - 1
- x - 12 = -10x + 6
Step 2: Get x-terms on same side of equation
- x + 10x = 6 + 12
9x = 18
Step 3: Get constants on same side of equation
9x = 18 - 0
9x = 18
Step 4: Get the x by itself by using the inverse operation
x = 18 / 9
x = 2
So, the solution to the equation is x = 2.
Match the description of the one variable equation with the number of solutions it will have.
ax+c1=bx+c2
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the
The number of x's on both sides of the equation is different a≠b
The number of x's is the same on both sides of the equation, and the constant is different a=b, c1≠c2
The number of x's is the same on both sides of the equation and the constant is also the same a=b, c1=c2
The number of x's on both sides of the equation is different a≠b
Order the steps for solving the equation: 2x−5=3(4x+5)
1. Distribute the 3 to the terms inside the parentheses on the right side of the equation: 2x - 5 = 12x + 15
2. Combine like terms on each side of the equation: 2x - 12x = 15 + 5
3. Simplify: -10x = 20
4. Divide both sides of the equation by -10 to isolate x: x = -2
Solving the inequality for x, which statement shows a good first step and which is the correct solution?
x−6<x4
(2 points)
A good first step for solving the inequality x-6 < x+4 would be to subtract x from both sides of the inequality to eliminate the variable term.
x - 6 - x < x + 4 - x
Simplifying, we get:
-6 < 4
The correct solution is that the inequality -6 < 4 is always true for any value of x.
To follow the steps in solving the equation 5x−12−6x=−10x+7−1, let's go through each step:
Step 1: Combine like terms
Combine the x-terms on both sides of the equation, which are 5x and -6x on the left side and -10x on the right side.
(5x - 6x) - 10x = -10x + 7 - 1
Step 2: Get x-terms on the same side of the equation
To get the x-terms on the same side, let's add 10x to both sides of the equation.
5x - 6x - 10x + 10x = -10x + 10x + 7 - 1
Simplifying both sides of the equation, we have:
5x - 6x - 10x + 10x = 0
Step 3: Get constants on the same side of the equation
Now, let's combine the constant terms. On the right side, we have 7 and -1.
0 = 7 - 1
Simplifying, we get:
0 = 6
Step 4: Get the x by itself by using the inverse operation
Since 0 does not equal 6, it means there is no solution for this equation. Therefore, there is no value for x that satisfies the original equation.
Thus, the final step is to conclude that the given equation has no solution.